{"title":"算术动力学中齐格蒙迪集大小的定量估算","authors":"Yang Gao, Qingzhong Ji","doi":"arxiv-2409.04710","DOIUrl":null,"url":null,"abstract":"Let \\( K \\) be a number field. We provide quantitative estimates for the size\nof the Zsigmondy set of an integral ideal sequence generated by iterating a\npolynomial function \\(\\varphi(z) \\in K[z]\\) at a wandering point \\(\\alpha \\in\nK.\\)","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"42 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantitative Estimates for the Size of the Zsigmondy Set in Arithmetic Dynamics\",\"authors\":\"Yang Gao, Qingzhong Ji\",\"doi\":\"arxiv-2409.04710\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let \\\\( K \\\\) be a number field. We provide quantitative estimates for the size\\nof the Zsigmondy set of an integral ideal sequence generated by iterating a\\npolynomial function \\\\(\\\\varphi(z) \\\\in K[z]\\\\) at a wandering point \\\\(\\\\alpha \\\\in\\nK.\\\\)\",\"PeriodicalId\":501035,\"journal\":{\"name\":\"arXiv - MATH - Dynamical Systems\",\"volume\":\"42 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Dynamical Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.04710\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04710","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
让 \( K \) 是一个数域。我们提供了在一个游走点 \(\alpha \inK.\)上迭代apolynomial函数 \(\varphi(z) \in K[z]\)所产生的积分理想序列的Zsigmondy集合大小的定量估计值。
Quantitative Estimates for the Size of the Zsigmondy Set in Arithmetic Dynamics
Let \( K \) be a number field. We provide quantitative estimates for the size
of the Zsigmondy set of an integral ideal sequence generated by iterating a
polynomial function \(\varphi(z) \in K[z]\) at a wandering point \(\alpha \in
K.\)
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